ECEG105/ECEU646 Optics for Engineers Course Notes Part 4: Apertures, Aberrations Prof. Charles A. DiMarzio Northeastern University Fall 2008 July 2003+ Chuck DiMarzio, Northeastern University 11270-04-1 Aug 2007 Sept 2008
Advanced Geometric Optics Introduction Stops, Pupils, and Windows f-number Examples Magnifier Microscope Aberrations Design Process From Concept through Ray Tracing Finalizing the Design Fabrication and Alignment July 2003+ Chuck DiMarzio, Northeastern University 11270-04-2
Some Assumptions We Made All lenses are infinite in diameter Every ray from every part of the object reaches the image Angles are Small: sin(θ)=tan(θ)=θ cos(θ)=1 July 2003+ Chuck DiMarzio, Northeastern University 11270-04-3
What We Have Developed Description of an Optical System in terms of Principal Planes, Focal Length, and Indices of Refraction These equations describe a mapping from object space (x,y,z) to image space (x,y,z ) s, s are z coordinates B H V V H B July 2003+ Chuck DiMarzio, Northeastern University 11270-04-4 Sept 2007 Sept 2008
Lens Equation as Mapping The mapping can be applied to all ranges of z. (not just on the appropriate side of the lens) We can consider the whole system or any part. The object can be another lens s', Image Dist., cm. 50 40 30 20 10 0 10 20 30 40 50 60 40 20 0 20 40 60 s, Object Dist., cm. L 4 f = 10 cm. L 1 L 2 L 3 L 4 July 2003+ Chuck DiMarzio, Northeastern University 11270-04-5 Sept 2008
Stops, Pupils, and Windows (1) Intuitive Description Pupil Limits Amount of Light Collected Window Limits What Can Be Seen Window Pupil July 2003+ Chuck DiMarzio, Northeastern University 11270-04-6
Stops, Pupils and Images in Object Space Entrance Pupil Limits Cone of Rays from Object Entrance Window Limits Cone of Rays From Entrance Pupil Windows (2) Physical Components Aperture Stop Limits Cone of Rays from Object which Can Pass Through the System Field Stop Limits Locations of Points in Object which Can Pass Through System Images in Image Space Exit Pupil Limits Cone of Rays from Image Exit Window Limits Cone of Rays From Exit Pupil July 2003+ Chuck DiMarzio, Northeastern University 11270-04-7 Sept 2008
Finding the Entrance Pupil Find all apertures in object space L 4 is L 4 seen through L 1 -L 3 L 1 L 2 L 3 L 4 Entrance Pupil Subtends Smallest Angle from Object L 3 L 4 L 1 L 2 L 3 is L 3 seen through L 1 -L 2 July 2003+ Chuck DiMarzio, Northeastern University 11270-04-8
Finding the Entrance Window Entrance Window Subtends Smallest Angle from Entrance Pupil L 3 L 4 L 1 L 2 Aperture Stop is the physical object conjugate to the entrance pupil Field Stop is the physical object conjugate to the entrance window All other apertures are irrelevant July 2003+ Chuck DiMarzio, Northeastern University 11270-04-9 Sept 2008
f=28 mm Field of View f=55 mm f=200 mm Film= Exit Window July 2003+ Chuck DiMarzio, Northeastern University 11270-04-10
Example: The Telescope Aperture Stop Field Stop July 2003+ Chuck DiMarzio, Northeastern University 11270-04-11
The Telescope in Object Secondary Space Primary Secondary Entrance Window Entrance Pupil July 2003+ Chuck DiMarzio, Northeastern University 11270-04-12
The Telescope in Image Space Primary Primary Secondary Exit Pupil Exit Window July 2003+ Chuck DiMarzio, Northeastern University 11270-04-13 Stopped 26 Sep 03
f-number & Numerical f-number Aperture Numerical Aperture f θ F A A 5 F D is Lens Diameter 4 f#, f-number 3 2 1 0 0 0.2 0.4 0.6 0.8 1 NA, Numerical Aperture July 2003+ Chuck DiMarzio, Northeastern University 11270-04-14
Importance of Aperture ``Fast System Low f-number, High NA (NA 1, f# 1) Good Light Collection (can use short exposure) Small Diffraction Limit (λ/d) Propensity for Aberrations (sin θ θ) Corrections may require multiple elements Big Diameter Big Thickness Weight, Cost Tight Tolerance over Large Area July 2003+ Chuck DiMarzio, Northeastern University 11270-04-15 Sept 2008
The Simple Magnifier A F A F July 2003+ Chuck DiMarzio, Northeastern University 11270-04-16
The Simple Magnifier (2) Image Size on Retina Determined by x /s No Reason to go beyond s = 250 mm Magnification Defined as No Reason to go beyond D=10 mm f# 1 Means f=10 mm Maximum M m =25 For the Interested Student: What if s>f? July 2003+ Chuck DiMarzio, Northeastern University 11270-04-17 Sept 2008
Microscope F F F F A A Two-Step Magnification Objective Makes a Real Image Eyepiece Used as a Simple Magnifier July 2003+ Chuck DiMarzio, Northeastern University 11270-04-18
Microscope Objective F F F F A A July 2003+ Chuck DiMarzio, Northeastern University 11270-04-19
Microscope Eyepiece F F F F A A 2 A 2 July 2003+ Chuck DiMarzio, Northeastern University 11270-04-20
Microscope Effective Lens H H 192 mm Barrel Length = 160 mm FA f f 1 =16mm 2 =16mm F Effective Lens: D f = -1.6 mm D 19.2 mm H H 19.2 mm F A F July 2003+ Chuck DiMarzio, Northeastern University 11270-04-21
Microscope Aperture Stop Analysis in Image Space F F Image Exit Pupil Aperture Stop =Entrance Pupil Put the Entrance Pupil of your eye at the Exit Pupil of the System, Not at the Eyepiece, because 1) It tickles (and more if it s a rifle scope) 2) The Pupil begins to act like a window July 2003+ Chuck DiMarzio, Northeastern University 11270-04-22 Sept 2008 Stopped here 30 Sep 03
Microscope Field Stop F F Entrance Window Field Stop = Exit Window July 2003+ Chuck DiMarzio, Northeastern University 11270-04-23
Microscope Effective Lens July 2003+ Chuck DiMarzio, Northeastern University 11270-04-24
Apertures Summary Object and Image Space Locating All the Elements Finding the Pupil Computing the Pupil Size and NA or f# Finding the Window Computing the Field of View July 2003+ Chuck DiMarzio, Northeastern University 11270-04-25 Dec 2004
Aberrations Failure of Paraxial Optics Assumptions Ray Optics Based On sin(θ)=tan(θ)=θ Spherical Waves φ=φ 0 +2πx 2 /ρλ Next Level of Complexity Ray Approach: sin(θ)=θ+θ 3 /3! Wave Approach: φ=φ 0 +2πx 2 /ρλ+cρ 4 +... A Further Level of Complexity Ray Tracing July 2003+ Chuck DiMarzio, Northeastern University 11270-04-26
Examples of Aberrations 1 (1) Paraxial Imaging 0.5 0 R = 2, n=1.00, n =1.50 s=10, s =10-0.5 m4061_3-1 -10-5 0 5 10 In this example for a ray having height h at the surface, s (h)<s (0). July 2003+ Chuck DiMarzio, Northeastern University 11270-04-27
Example of Aberrations 0.2 0.15 0.1 0.05 z(h=1.0) z(h=0.6) (2) Longitudinal Aberration = z Transverse Aberration = x 0-0.05-0.1 Where Exactly is the image? -0.15 2 x(h=1.0) m4061_3-0.2 8.5 9 9.5 10 10.5 What is its diameter? July 2003+ Chuck DiMarzio, Northeastern University 11270-04-28
Spherical Aberration Thin Lens in Air July 2003+ Chuck DiMarzio, Northeastern University 11270-04-29
Transverse Spherical Aberration h s x s(0) July 2003+ Chuck DiMarzio, Northeastern University 11270-04-30
Evaluating Transverse SA July 2003+ Chuck DiMarzio, Northeastern University 11270-04-31
Coddington Shape Factors -1 p=0 +1 q=0-1 +1 July 2003+ Chuck DiMarzio, Northeastern University 11270-04-32
Numerical Examples 5 Beam Size, m 10-2 s=1m, s =4cm q, Shape Factor 0-5 -1-0.5 0 0.5 p, Position Factor n=1.5 n=2.4 n=4 10-3 10-4 10-5 10-6 n=2.4 n=4 n=1.5 DL at 10 µm DL at 1.06 µm 500 nm -5 0 5 q, Shape Factor July 2003+ Chuck DiMarzio, Northeastern University 11270-04-33 1
Phase Description of Aberrations v y Object Entrance Pupil Exit Pupil Image z Mapping from object space to image space Phase changes introduced in pupil plane Different in different parts of plane Can change mapping or blur images July 2003+ Chuck DiMarzio, Northeastern University 11270-04-34 Sept 2008
Coordinates for Phase v y z v v Analysis phase Solid Line is phase of a spherical wave toward the image point. Dotted line is actual phase. Our goal is to find (ρ,φ,h). 2a ρa u 0<ρ<1 y h x July 2003+ Chuck DiMarzio, Northeastern University 11270-04-35
Aberration Terms Odd Terms involve tilt, not considered here. Δ=ρ cosφ July 2003+ Chuck DiMarzio, Northeastern University 11270-04-36
Second Order Image Position Terms: The spherical wave is approximated by a second-order phase term, so this error is simply a change in focal length. July 2003+ Chuck DiMarzio, Northeastern University 11270-04-37
Fourth Order (1) ρ 2 is focus: depends on h 2 and h 2 cosφ Spherical Aberration Astigmatism and Field Curvature Tangential Plane T S Sagittal Plane Sample Images At T At S July 2003+ Chuck DiMarzio, Northeastern University 11270-04-38 Sept 2008
Fourth Order (2) ρ cosφ is Tilt: Depends on h 3 Coma y v Barrel Distortion Pincushion Distortion u x July 2003+ Chuck DiMarzio, Northeastern University 11270-04-39 Sept 2008
Optical Design Process July 2003+ Chuck DiMarzio, Northeastern University 11270-04-40
Ray Tracing Fundamentals July 2003+ Chuck DiMarzio, Northeastern University 11270-04-41
If One Element Doesn t Add Another Lens Work... Let George Do It Different Index? Smaller angles with higher index. Thus germanium is better than ZnSe in IR. Not much hope in the visible. Aspherics July 2003+ Chuck DiMarzio, Northeastern University 11270-04-42
Aberrations Summary Origin of Aberrations On-Axis Aberrations Change of Focus Spherical Aberration Off-Axis Aberrations Additional Blurring Effects Distorting Effects July 2003+ Chuck DiMarzio, Northeastern University 11270-04-43 Dec 2004
Summary of Concepts So Far Paraxial Optics with Thin Lenses Thick Lenses (Principal Planes) Apertures: Pupils and Windows Aberration Correction Analytical Ray Tracing What s Missing? Wave Optics July 2003+ Chuck DiMarzio, Northeastern University 11270-04-44